# GEOMETRY OF FORMS

Most design themes, including those described in this book, are strongly related to two fundamental geometric shapes: the circle and the square. Visually pleasing design compositions are usually based on sensitive relationships between these two shapes (or their component parts), whereas visually disturbing compositions fail to consider them. It is important to understand these two forms when creating a design composi­tion because both shapes have a number of inherent geometric characteristics and components that influence their use in design.

The Circle

Among the many and varied forms we see in the world around us, the circle stands out as being unique. Because of its simplicity and completeness, the circle has often been described as the most pure or perfect form.

The circle has a number of components that are critical to its use in a design composition. These are the (1) center, (2) circumference, (3) radii, (4) extended radii, (5) diameter, and (6) tangent (Figure 10—4). The center is, of course, the middle point

of the circle. It is the place where all radii and diameters meet and/or cross each other. The circumference, or outer edge of the circle, defines the limits or edge of the circle. Radii are lines that originate at the center of the circle and extend outward to the cir­cumference. Extended radii are similar, but extend beyond the circle’s circumference. The diameter is a line that extends from one side of the circle to the other and passes directly through the center. A tangent is a line that touches the circumference while also establishing a right angle (90 degrees) with a radius.

Among all the circle’s component parts, the center is perhaps the most impor­tant of all. First, the center is a point that inherently attracts attention. Most people can estimate the location of the center of a circle rather easily with a pencil or pen. Furthermore, the radii, extended radii, and diameters pass through the center, rein­forcing its position and importance. So, one of the first considerations for designing with a circle is to realize that any line that directly points to a circle’s center will create a strong relationship with the circle (right side of Figure 10—5). Lines that don’t point to the circle’s center are apt to seem awkward or unrelated in their relationship with the circle (left side of Figure 10—5).

In a similar fashion, the manner in which lines and forms meet the circle’s cir­cumference helps determine whether or not a composition is successful. Those com­positions in which lines meet the circle’s circumference by utilizing an extended ra­dius are apt to be more pleasing than those that don’t (Figure 10—6). In other words, lines and edges that form a 90-degree relationship to a circle’s circumference are more stable looking than compositions that lack this relationship.

Because design involves the development of alternative ideas, it is important to realize that numerous design compositions can be generated by exploring the relation­ships possible among the basic components of a specific form. Each of the circle’s components has the potential of becoming a form generator when combined with an­other component. Many design ideas are possible that use two, three, four, or all five of the circle components (Figure 10—7). This type of activity can stimulate design cre­ativity and make designing an exciting process.

Equilateral polygons can be used in developing design compositions and can be formed within a circle. The forms presented here are (1) triangle (three sides), (2) square (four sides), (3) pentagon (five sides), (4) hexagon (six sides), and (5) octagon (eight sides).

Figures 10—8 through 10—12 illustrate how each of these polygons is formed within a circle, respectively.

Updated: October 11, 2015 — 2:02 am